Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
Contents lists available at ScienceDirect
Journal of Quantitative Spectroscopy &
Radiative Transfer
journal homepage: www.elsevier.com/locate/jqsrt
Ice cloud single-scattering property models with the full phase
matrix at wavelengths from 0.2 to 100 mm
Bryan A. Baum a,n, Ping Yang b, Andrew J. Heymsfield c, Aaron Bansemer c,
Benjamin H. Cole b, Aronne Merrelli a, Carl Schmitt c, Chenxi Wang d
a
SSEC, University of Wisconsin-Madison, 1225 W. Dayton Street, Madison, WI 53706, United States
Texas A&M University, College Station, TX, United States
National Center for Atmospheric Research, Boulder, CO, United States
d
Earth System Science Interdisciplinary Center, University of Maryland, College Park, MD, United States
b
c
a r t i c l e i n f o
abstract
Article history:
Received 4 November 2013
Received in revised form
7 February 2014
Accepted 26 February 2014
Available online 11 March 2014
Ice cloud bulk scattering models are derived for 445 discrete wavelengths between 0.2 mm
and 100 mm. The methodology for deriving these optical models is based on microphysical
data from 11 field campaigns using a variety of in situ probes, and incorporates a
correction to mitigate the impact of ice particles that shatter at the probe inlets. The
models are also based on a new library of ice habit single scattering properties developed
for plates, droxtals, hollow and solid columns, hollow and solid bullet rosettes, an
aggregate of solid columns, and a small/large aggregate of plates. Three sets of models
are developed that assume the use of solid columns only, the aggregate of solid columns
only, and a general habit mixture that incorporates all the habits. The consistency of the
resulting models is explored. While the general habit mixture provides consistency with
in situ microphysical measurements and the closest agreement with polarized reflectivities observed by the POLDER instrument on the PARASOL satellite, the aggregate of
severely roughened solid columns provides the closest agreement between solar and
infrared optical thicknesses. Finally, spectral results are presented for the shortwave and
longwave models.
& 2014 Elsevier Ltd. All rights reserved.
Keywords:
Ice clouds
Light scattering
Remote sensing
Radiative transfer
1. Introduction
The inference of cloud macrophysical, microphysical,
and optical properties for a given sensor generally requires
a comparison of sensor measurements to shortwavechannel reflectivities and/or longwave-channel brightness
temperature (BT) simulations for a set of known surface
and atmospheric conditions. The measurements may be at
high spectral resolution or for a set of narrowband or
n
Corresponding author. Tel.: þ 1 608 263 3898; fax: þ 1 608 262 5974.
E-mail address: bryan.baum@ssec.wisc.edu (B.A. Baum).
http://dx.doi.org/10.1016/j.jqsrt.2014.02.029
0022-4073 & 2014 Elsevier Ltd. All rights reserved.
broadband channels, and may further include polarization.
In fact, measurements encompassing all of these characteristics are, or were at one time, provided by passive
sensors flying in formation as part of the NASA Earth
Observing System A-Train constellation. New instruments
are being developed and tested on aircraft or groundbased systems that further extend the range of the
measurements.
The physical retrieval approach for inferring ice cloud
parameters, e.g., cloud thermodynamic phase and optical
thickness, relies on the use of a radiative transfer model
to simulate accurately the cloud radiances for a variety
of different conditions. The cloud radiance simulations
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B.A. Baum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
require a set of single scattering properties, including the
single scattering albedo, extinction coefficient, and the
scattering phase function (i.e., the first element of the
phase matrix). Additionally, the full phase matrix is
required for polarization simulations.
The goal of this study is to document a set of ice cloud
bulk models that provide these single scattering properties
consistently over a wide wavelength range from the ultraviolet (UV) through the far infrared (Far-IR). The current
effort expands upon the derivation of ice cloud bulk singlescattering models at solar wavelengths [1] based on in situ
cloud microphysical measurements and single-scattering
calculations for different ice habits. While the methodology adopted here is the same as in [1], the models now
encompass wavelengths from 0.2 to 100 mm. The single
scattering properties are given with respect to the effective
diameter (Deff), which is proportional to the ratio of the
total volume to the total projected area and is defined in
Appendix A. Note that the effective diameter is a parameter
used in modern climate models to specify the mean size of
cloud particles. The use of the effective particle size is now
broadly accepted in the radiative transfer community [2].
A key feature of the effective diameter is that the details of
the particle size distribution (PSD) are not significant for
specifying the bulk radiative properties [3,4].
In turn, the bulk properties are employed in a radiative
transfer model to simulate cloud reflectivity and transmission properties for a wide range of conditions (including
variations in cloud height, viewing geometry, optical
thickness, and effective particle size). Ice cloud optical
thickness and effective particle size are inferred by comparing measurements to simulations. The retrieval techniques may use data from solar channels [5–9], infrared (IR)
channels [10,11], IR spectra [12,13], polarized reflectivity
data [14–17], or combinations thereof [18–20]. While
many algorithms are available to infer these ice cloud
properties, the question arises as to the consistency of the
properties between these different sensors. This question
is relevant for studies involving long-term cloud characteristics because there may be gaps in the measurements
from any given wavelength region.
Our motivation for continuing the effort to develop bulk
scattering property models is that the ice cloud optical
thickness inferred from different sensors tends to be inconsistent. For example, Baum et al. [21] noted that the optical
thickness values inferred from solar channel data collected
during the SUbsonic aircraft Contrail and Clouds Effects
Special Study (SUCCESS) field campaign were higher than
those obtained from infrared (IR) channels. Comparisons of
cirrus optical thickness (τo3) between the MODerateresolution Imaging Spectroradiometer (MODIS) Collection 5
products [7] and active measurements from Cloud-Aerosol
Lidar with Orthogonal Polarization (CALIOP, [22,23]) indicate
significant differences, with MODIS being higher relative to
CALIOP. Zhang et al. [24] investigate differences between
MODIS Collection 5 and POLDER optical thickness retrievals,
and relate the differences to the assumed scattering properties adopted by each team.
This study summarizes the numerous research advancements that are included in this comprehensive set of ice
cloud bulk scattering property models. Results are presented
for spectral models at wavelengths from 0.2 to 100 mm that
include the full phase matrix. The models include ice particle
roughening, which can impact the phase matrix [25]. Models
have also been developed for polar-orbiting and geostationary imagers that account for the individual sensor spectral
response functions. The goal is to provide models that are
built for each sensor using consistent and straightforward
methodology.
The single-scattering properties in the spectral models
consist of the single-scattering albedo, asymmetry parameter, extinction coefficient, extinction efficiency, total
projected particle area, and the full phase matrix,
all as functions of the effective diameter. For the various
imagers, only the scattering phase function (i.e., P11) is
provided. This new generation of ice cloud models is
anticipated to provide a significant improvement in consistency between sensors over the previous versions. The
differences between optical thickness retrievals based on
solar and IR techniques will be reduced, as will optical
thickness differences between passive and active sensors.
Furthermore, the new models are more consistent with
polarized reflectivity measurements from sensors such as
PARASOL [26].
Section 2 discusses the microphysical data and the
library of ice particle single-scattering properties used in
the study. Also discussed in this section is the approach
adopted to develop both spectral and narrowband bulk
single-scattering properties from the microphysical data
and ice particle single-scattering property library. Models
are developed for three choices of the ice habit: (1) a
general habit mixture, (2) solid columns only, and (3)
aggregate of solid columns only. Section 3 provides a sense
of the consistency of the new ice models. Ice cloud optical
thickness is evaluated from comparing solar and infrared
(IR) techniques, and also comparing to historical MODIS
Collection 5 ice cloud optical thickness. Results from the
new models across the spectrum from the UV to the Far-IR
are presented in Section 4, and Section 5 concludes.
2. Data and models
2.1. Microphysical data
The microphysical data provide information on particle
size distributions (PSDs) as well as the ice water content
(IWC) and the median mass diameter (Dmm, i.e., the
diameter at which half the mass in the PSD is in smaller
particles and half in larger particles). The data are based on
a series of ice cloud field campaigns listed in Table 1.
A detailed summary of these data is provided in [27] and
Table 1 provides information on the location of the 11 field
campaigns and the sensors used for measuring the particle
size spectra. The field campaigns were held in a variety
of midlatitude and tropical locations, including sites
from both the hemispheres. The fitting coefficients for
the gamma distribution are provided for each individual
particle size distribution (PSD), as well as the maximum
diameter that should be used for the spectra. The maximum diameter is the size of the largest observed particle,
which is partially dependent on the sensor used to derive
the specific dataset.
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B.A. Baum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
Table 1
More than 14,000 PSDs are used in this study after filtering the total sample set such that the cloud temperature T r " 40 1C. The data are revised to reflect
better consistency between probes and to account for refinement of processing procedures. The field campaigns include the Atmospheric Radiation
Measurement program Intensive Observation Period (ARM-IOP); Tropical Rainfall Measuring Mission (TRMM); Cirrus Regional Study of Tropical Anvils and
Cirrus Layers Florida Area Cirrus Experiment (CRYSTAL-FACE); Aura Validation Experiment (pre-AVE, 2004); Midlatitude Cirrus Experiment (MidCiX,
2004); Stratospheric-Climate links with emphasis On the Upper Troposphere and lower stratosphere (SCOUT); Aerosol and Chemical Transport in tropIcal
conVEction (ACTIVE); Mixed Phase Arctic Cloud Experiment (MPACE); and Tropical Clouds, Convection, Chemistry, and Climate (TC4). The different probe
types include the 2-Dimensional Cloud probe (2-DC), the 2-Dimensional Precipitation probe (2-DP), the Cloud Particle Imager (CPI), the Video Ice Particle
Sampler (VIPS), the Precipitation Imaging Probe (PIP), the Cloud, Aerosol, and Precipitation Spectrometer (CAPS), and the Forward Scattering Spectrometer
Probe (FSSP). Ice water content measurements are from the Counterflow Virtual Impactor (CVI), the Closed-path tunable diode Laser Hygrometer (CLH), or
the Harvard University Lyman-α total water photofragment-fluorescence hygrometer (HT), and m-D refers to when a mass dimensional relationship was
used to estimate the ice water content.
Field campaign
Year
Location
Number of 5-s averaged
PSDs Tcld r " 40 1C
Probes
IWC
ARM IOP
TRMM KWAJEX
CRYSTAL-FACE (from WB-57)
SCOUT
ACTIVE-Monsoons
ACTIVE-Squall Lines
ACTIVE-Hector
MidCiX
Pre-AVE
MPACE
TC-4
2000
1999
2002
2005
2005
2005
2005
2004
2004
2004
2007
Oklahoma, USA
Kwajalein, Marshall Islands
Caribbean
Darwin, Australia
Darwin, Australia
Darwin, Australia
Darwin, Australia
Houston, TX USA
Houston, TX, USA
Prudhoe Bay, Alaska
Costa Rica
1420
201
221
358
4268
740
2583
2968
99
671
877
2D-C, 2D-P, CPI
2D-C, HVPS, CPI
CAPS, VIPS
FSSP, 2D-C
CAPS
CAPS
CAPS
CAPS, VIPS
VIPS
2D-C, CPI
CAPS, PIP
CVI
m-D
CLH
m-D
m-D
m-D
m-D
CLH
HT
m-D
CVI
The sets of available PSDs listed in the table are filtered
such that Tcld r " 40 1C to ensure that we are working with
ice cloud measurements. Even with this conservative
temperature filter, more than 14,000 PSDs remain and
are used in this study. For perspective, these PSD measurements are taken from over 70,000 km of flight tracks.
These data encompass both convective outflow and stratiform ice clouds, with IWC values spanning six orders of
magnitude from 10 " 6 to 100 g m " 3. The IWC is obtained
from direct measurements or by applying a mass–dimensional relationship [27]. The approach of Schmitt and
Heymsfield [28] is used for high altitude cases.
For ice clouds that contain large particles, it has been
shown that small particle concentration measurements
are influenced by shattering at the inlet of the 2D-C (and
similar) probes [29–31]. Since the data used here are
filtered for very cold clouds (Tcld r " 40 1C), particle shattering should not generally be a large problem due the lack
of very large particles except in cases of deep convection.
Where shattering is a problem, it is most evident in the
total concentration measurement since total concentration
is usually dominated by the smallest particles. However,
the effect of shattering is diminished when the PSD is
weighted to larger particle sizes, such as in computing
IWC, Dmm, or any other higher moment and when dividing
two moments of similar magnitudes such as in deriving
the effective radius [31]. The data used in this study were
reprocessed to mitigate the shattering issue for all the 2D
probe data as described by Field et al. [31]. Also, we note
that small particle data were obtained by balloon borne
replicators for ARM and small particle probes were used
for SCOUT where only small particles were observed. For
the other field programs, small particles had little contribution [32].
The microphysical data for all PSDs used in this study
are available for electronic download through the link
provided in Table 2.
2.2. Ice particle single scattering properties
The single-scattering properties are provided in a
database [33] for nine different ice particle habits: droxtals, plates, solid and hollow columns, solid and hollow
bullet rosettes, an aggregate of solid columns, and both a
small and large aggregate of plates. The ice habit singlescattering properties are based on a combination of the
Amsterdam Discrete Dipole Approximation (ADDA), the
T-matrix method, and the improved geometric-optics
method (IGOM) [33]. The single-scattering properties are
provided for each habit at 189 discrete sizes between 2
and 10,000 mm and for 445 discrete wavelengths ranging
from 0.2 to 100 mm. The 445 discrete wavelengths are
defined as follows. For this study, the properties are
interpolated at a 0.01–mm resolution at wavelengths
between 0.2 and 3 mm (280 discrete wavelengths) and at
a 0.1-mm resolution between 3 and 15 mm (120 discrete
wavelengths). The remaining 45 discrete wavelengths are
defined between 16 and 100 mm at the inflection points of
the imaginary index of refraction (as shown in [33]). The
single scattering properties can be interpolated if properties are desired at different wavelengths.
A summary of the primary improvements in the accuracy of the single-scattering properties is as follows:
# The accuracy of the extinction and absorption efficiencies
#
#
at moderate to large size parameters is improved due to
the use of an empirical approach to include the edge and
the above/below-edge effects on ice particles [33].
Recent studies discuss the impact of surface roughening on ice particle properties inferred from measurements [34,35]. In this study, three surface roughness
conditions are considered: smooth, moderately roughened, and severely roughened particles [36].
A new analytical treatment of forward scattering in the
IGOM renders obsolete the delta transmission energy
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Table 2
Links to the microphysical data, spectral models, and narrowband models.
Data or model
Link
Comments
Microphysical data
Spectral models from 0.2 to 100 mm
Narrowband models for various sensors
http://www.ssec.wisc.edu/ice_models/microphysical_data.html
http://www.ssec.wisc.edu/ice_models/polarization.html
http://www.ssec.wisc.edu/ice_models/imager.html
For field campaigns in Table 1
At 445 individual wavelengths; NetCDF
For sensors in Table 3; NetCDF
Table 3
Satellite sensors for which narrowband models are available. The models are built with the general habit mixture and assume that the particles are severely
roughened.
Satellite imager
Platforms
Name and notes
AVHRR
MODIS
MISR
AATSR
IIR
VIIRS
ATSR
SEVIRI
GOES
MTSAT
GOES ABI
NOAA 5–19; MetOP A/B
Terra/Aqua
Terra
Advanced Very High Resolution Radiometer
Moderate Resolution Imaging Spectroradiometer
Multiangle Imaging SpectroRadiometer
Advanced Along-Track Scanning Radiometer
Imaging Infrared Radiometer
Visible Infrared Imaging Radiometer Suite
Along Track Scanning Radiometer
Spinning Enhanced Visible and InfraRed Imager
Geostationary Operational Environmental Satellite
Multifunctional Transport Satellites
Advanced Baseline Imager;
New series of GOES; set to launch in 2015
#
#
#
CALIPSO
Suomi-NPP
Imager 1–2
METEOSAT Second Generation
GOES–8 through GOES–13
1–2
GOES-R
term [37]. This term was an artifact of the numerical
treatment of forward scattering in earlier studies [38].
The extinction efficiency does not have a constant value
of 2 in the current version of IGOM and now considers
the variation of the extinction efficiency as a function of
size parameter [33].
The single-scattering calculations are based on an
updated compilation of the real and imaginary parts
of the refractive index for ice [39].
The phase matrix elements for randomly oriented ice
particles are provided in the database.
2.3. Ice particle general habit mixture
A general habit mixture (GHM) scheme that incorporates all the nine available ice particle habits [1,26] is
adopted here with minor changes to the percentages of
habits in the smallest size bins. The percentage of droxtals
was decreased slightly in favor of increasing plates, columns, and rosettes. The maximum diameter permitted for
plates, solid columns, and hollow columns is 500 mm. The
hollow/solid bullet rosettes and the three aggregate habits
are used for the largest particles in a size distribution. The
fraction of a given habit changes linearly with size so as to
minimize abrupt changes in average single-scattering
properties across size boundaries. Each PSD has an upper
limit for the maximum size particle used in its derivation,
so the largest size particles may not be used for many of
the extremely cold clouds where only smaller sizes exist.
2.4. Spectral models
Ice cloud bulk scattering models are developed for
a given wavelength by integrating over both particle size
and habit distributions for a given wavelength as shown in
Appendix A. This process results in a set of over 14,000
calculations of the single scattering properties for every
wavelength provided in the single-scattering property
database. While this might seem abundant, there are
retrieval approaches that require estimates of the variability of the individual single scattering properties. Such
variability can be used in optimal estimation applications
or described in terms of Jacobians (i.e., partial derivatives)
for data assimilation studies.
From this full set of calculations, the single scattering
properties are averaged in narrow intervals about selected
Deff values to make a limited set of models that is more
manageable for radiative transfer calculations. The singlescattering albedo, asymmetry parameter, extinction coefficient, extinction efficiency, total projected particle area,
and phase matrix are provided as functions of the effective
diameter that ranges from 10 to 120 mm in increments of
5 mm for a total of 23 individual Deff values.
The spectral models of bulk ice cloud single-scattering
properties discussed in this and following sections are
available for electronic download through the link provided in Table 2.
2.5. Imager (narrowband) models
Narrowband models are calculated by integrating the
spectral models over a wavelength interval encompassed
by a given imager spectral response function. The integration details are provided in Appendix A. The narrowband
models of bulk ice cloud single-scattering properties are
available for electronic download through the link provided in Table 2. Table 3 lists the imager models currently
available.
B.A. Baum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
3. Evaluation of model consistency
One of our goals is to work towards a single-scattering
property model that improves the consistency in the remote
sensing of ice cloud properties between different sensors.
This is currently an issue, as shown in a study that compared
ice cloud optical thickness retrievals between POLDER and
MODIS Collection 5 products [24] that revealed significant
differences. The differences were attributed to the assumed
single scattering properties. The MODIS Collection 5 models
assume smooth ice particles and the POLDER model employs
the Inhomogeneous Hexagonal Monocrystal (IHM) model
[17]. The IHM model introduces inhomogeneities within the
particle, resulting in a featureless scattering phase function
(i.e., no halos or other maxima other than the forward
scattering peak) as well as a lower asymmetry parameter
than a smooth particle model.
One way of evaluating the consistency of the ice models
is by imposing a set of constraints. In this section, three
questions are discussed in further detail: (1) are the model
microphysical properties (IWC and Dmm) derived from the
simulated ice habits similar to those from the in situ
measurements, (2) do simulated polarized reflectivities
based on the ice models compare reasonably well to those
from PARASOL measurements of ice clouds over ocean,
and (3) are the optical thickness values consistent when
inferred from solar and IR wavelengths?
127
Models based solely on solid columns are used to
derive CERES cloud products [9]. Recently, aggregates of
solid columns were adopted for deriving MODIS Collection
6 cloud products rather than a habit mixture as adopted
for Collection 5. There are evidently many points of view
to consider when choosing a habit or habit mixture for the
ensuing global operational data reduction. The habit
mixture captures more of the complexity of natural ice
clouds than adopting a single habit. However, what really
matters is whether the habit choice is sufficient for a given
application. Some constraints to consider when choosing a
habit model are discussed in more detail below.
Results are presented in this and following sections
based on the GHM and two individual habits: aggregates
of solid columns (ASC) and solid columns (SC). To be clear,
the ASC and SC models employed in the following analyses
are not the same models adopted by the CERES or MODIS
teams, but are our own models based on these individual
habits.
3.1. Comparison of computed to measured
microphysical properties
The bulk properties are computed for each PSD by
integrating the individual habit properties over the size
range for an assumed habit profile [1]. Details are provided
Fig. 1. Comparison of calculated to measured ice water content (IWC) for each of the particle size distributions listed in Table 1, assuming the use of
(a) solid columns only, (b) aggregate of solid columns only, and (c) a general habit mixture.
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in Appendix A to show how the microphysical properties of
IWC and Dmm are estimated from the ice habits and PSDs.
Fig. 1 shows a comparison of the measured to calculated
IWC values for the individual PSDs from the various field
campaigns listed in Table 1. Since field campaigns provide
invaluable data for validating satellite products, the goal is
for IWC to compare reasonably well to those values provided
from the in situ measurements. The comparisons from the SC
provide the closest match (Fig. 1a), while the ASC results
have a higher bias at low IWC values than at higher IWC
values. The ASC was intended for use as a large ice particle;
for very small particles diameters, the columns are so small
that the particle has a lower volume than some of the other
habits such as the droxtal and column, leading to lower
values of the IWC. The GHM compares reasonably well with
the IWC values over much of the range.
Fig. 2 shows the comparison of Dmm between the
calculated values and those derived from the in situ
measurements. Again, the SC results (Fig. 2a) provide
the closest comparison with the in situ measurements.
However, the adoption of the ASC results in a general
overestimation of Dmm for the reason discussed previously;
at small sizes, the columns in the aggregate are very
small, leading to low volumes and hence mass per particle.
The GHM results compare favorably with the in situ
measurements at Dmm values lower than about 400 mm,
but overestimate the Dmm at higher values.
3.2. Comparison of model to PARASOL polarized reflectivities
The issue of particle roughening discussed earlier raises
a number of questions as it impacts the various phase
matrix components [25]. Since halos are often observed,
one can make the argument that there are times for which
at least some of the ice particles in a given distribution are
smooth and fairly free of internal inhomogeneities. If
roughening is to be used as a surrogate for all the internal
inhomogeneities, incomplete facets, and surface characteristics for a distribution of ice particles, how much roughening is appropriate for use with global satellite retrievals?
Polarized reflectivity measurements provide a unique
perspective to the issue of particle roughening. In a study
that compared model-simulated polarized reflectivities to
PARASOL measurements over ocean [26], it was shown that
in addition to the general habit mixture, there are several
individual habits that can match the PARASOL measurements closely, e.g., the hollow 3D bullet rosette, the hollow
column, and the small aggregate of plates (cf. Fig. 6 of that
study). The use of the general habit mixture and the
assumption of severe particle roughening leads to the
closest comparison with measured polarized reflectivities
over a range of side to back-scattering angles. The following
results are an extension of this earlier work, and assume the
presence of severe roughening, thereby forgoing further
discussion of smooth or moderately roughened particles.
Fig. 2. Comparison of calculated to measured median mass diameters (Dmm) for each of the particle size distributions listed in Table 1, assuming the use of
(a) solid columns only, (b) aggregate of solid columns only, and (c) a general habit mixture.
B.A. Baum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
129
Fig. 3. A comparison of normalized polarized reflectivities obtained from one day of PARASOL data over ocean (1 August, 2007) in the color contours
to calculations (black dots) based upon an ice cloud model built assuming a single habit of solid columns (SC) for effective diameters (Deff) of (a)
10 mm, (b) 30 mm, (c) 50 mm, and (d) 70 μm. The PARASOL color contours represent the frequency of occurrence for a given reflectivity, with the
red color denoting the region having the highest occurrences for the day of data. The variability in the calculated polarized reflectivities occurs because a
large range of viewing angle combinations (solar zenith, viewing zenith, and relative azimuth) was used, and many combinations of these angles can result
in a similar scattering angle. Note that the black dots do not tend to match the PARASOL polarized reflectivities very closely over the range of scattering
angles.
The simulations based on the SC model are compared
to a day of PARASOL polarized reflectivities as shown in
Fig. 3. The four panels correspond to the use of different SC
model Deff values of 10 mm, 30 mm, 50 mm, and 70 mm.
In this figure, the color contours represent the frequency of
occurrence of PARASOL polarized radiances for ice clouds
from August 1, 2007, over ocean from 601N to 601S. The red
contour represents a region of high occurrence for the
measured radiances and the blue contour represents a
region of very low occurrence. The figure also shows a set
of black dots; each black dot represents a model calculation for a given set of viewing angles (solar zenith, viewing
zenith, and relative azimuth) provided in the PARASOL
data, with the further assumption that there is an ice cloud
with an optical thickness of 5, i.e., an ice cloud with a high
enough optical thickness so that the polarized reflectivity
is saturated. The polarization signal decreases because of
multiple scattering as optical thickness increases. Note
that the simulations do not match the PARASOL data very
closely for any of the Deff values, especially at side scattering angles.
Fig. 4 shows similar results but based on the ASC model.
At no Deff value do the simulations match well with the
measurements over the range of scattering angles. For all Deff
values, the polarized reflectivities calculated from the ASC
model tend to be lower than the measurements except near
backscattering angles. While not shown, the comparison
between simulated and measured polarized reflectivities is
not favorable based on models that assume an individual
habit.
Cole et al. [26] demonstrated that use of the GHM for a
range of Deff values resulted in consistent comparisons
with measured reflectivities for a single day of global data
over ocean (see Fig. 5 of [26]). A question that was not
addressed is whether these same models will result in
consistent comparisons with PARASOL over time. Fig. 5
shows similar comparisons for one day in each of the four
different seasons, based on the GHM for Deff ¼60 μm.
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B.A. Baum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
Fig. 4. Same as Fig. 3 but assuming the use of only the aggregate of solid columns. Results are shown for (a) Deff ¼10 μm, (b) Deff ¼ 30 μm, (c) Deff ¼50 μm,
and (d) Deff ¼70 μm. Note that the simulations (black dots) again do not tend to match the PARASOL polarized reflectivities very closely, especially at side
scattering angles.
The simulations generally match well with PARASOL
measurements over the range of scattering angles for each
of these days. It would be interesting to focus more
specifically on optically thin cirrus in future comparisons,
since the assumption made in the simulations is that
the ice clouds are optically thick from a polarization
perspective.
However, the general habit mixture compares closely to
the measured IWC and Dmm in the in situ measurements as
shown in the previous section. The closest match between
simulations and measurements occurred for particles that
were severely roughened with s ¼0.5.
In a new study, Cole et al. [40] perform multiple
retrievals for each PARASOL pixel and test individual habit
models as well as the habit mixture for a range of roughening values. Surprisingly, the aggregate of solid columns
is determined to be the preferred habit in the tropics,
although with a lower roughening value of s ¼0.2, while
more pristine particles are preferred at higher latitudes. It
may be that with ice clouds formed from deep convection,
the particles near cloud top have more irregularities (i.e.,
roughening) than ice particles that form in synoptic cirrus
at higher latitudes that have much lower updraft
velocities. Our results suggest that none of the nine
individual habit models can match adequately the polarized reflectivities observed in global data.
The information in polarized reflectivity measurements
is primarily useful for stratiform cirrus rather than deep
convective clouds. The reason is that the polarization
signal decreases with multiple scattering, so the interpretation of the data most likely corresponds to the upper
portions of the ice clouds. Clearly more research needs to
be done in this area to resolve some of these questions.
3.3. Comparison of solar to IR optical thicknesses
Another way to assess the consistency of cirrus optical
thickness (τ) retrievals is to compare results obtained
separately using solar and IR measurements. A case study
is provided to illustrate the solar and IR τ retrievals for a
MODIS–Aqua granule recorded over the Bay of Bengal at
0745 UTC on 2 August, 2010 as shown in Fig. 6.
For this analysis, two different fast models are
employed to infer optical thickness. The solar-based
method [41] infers optical thickness τ by minimizing the
differences between model simulations and observations
B.A. Baum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
131
Fig. 5. Comparison of PARASOL measurements of ice cloud polarized reflectivities over ocean (in the color contours) with simulations (black dots) based
on ice model bulk scattering properties developed using a general habit mixture (GHM) assuming Deff ¼ 60 μm for one day in four seasons: (a) 1 January,
2007, (b) 1 April, 2007, (c) 1 August, 2007, and 15 October, 2007. Note that the black dots mimic the PARASOL polarized reflectivities consistently for all
four days.
Fig. 6. Aqua/MODIS scene from 2 August, 2010, recorded over the Bay of
Bengal at 0745 UTC.
at 0.86 and 2.13 mm (MODIS bands 2 and 7, respectively).
The IR-based method [42] computes optical thickness
by minimizing the difference between measured and
computed radiances in the 8.5, 11, and 12 mm bands
(MODIS bands 29, 31, and 32 respectively).
A brief description of how the models are used is as
follows. The IR fast model simulates top-of-atmosphere
brightness temperatures (BTs) for three MODIS channels
by using different τ-Deff pairs. The retrieval begins from a
set of model simulations at m τ values and n Deff values.
A search is made through each of the m % n τ-Deff pairs
to determine which pair has the minimum modelobservation differences (or cost function). Based on this
initial τ-Deff pair, the program refines the τ-Deff search by
searching approximately 100 different τ-Deff pairs within a
small interval, and the τ-Deff pair with the minimum cost
function is considered to be the final result. The solar
model employs a similar methodology but is based on
channel reflectivities.
Fig. 7 shows comparisons of the IR-based optical thickness retrievals for the three different habit models. The
comparisons are shown as histograms of frequency of
occurrence for optical thickness values on a log 10 scale,
with red indicating the highest frequencies of occurrence.
Histograms are shown based on comparisons between (a)
the GHM and the ASC, (b) the solid column and the ASC
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B.A. Baum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
Fig. 7. Comparison of ice cloud optical thicknesses based on a fast model that minimizes the differences between measured and computed radiances in the
8.5, 11, and 12 mm bands (MODIS bands 29, 31, and 32 respectively). The IR optical thicknesses are based on different ice habit models for the MODIS
granule shown in Fig. 3. Histograms are shown based on results (a) for the general habit mixture and the aggregate of solid columns, (b) the solid column
and the aggregate of solid column models, and (c) the general habit mixture and solid column models. The histograms show frequencies of occurrence on a
log 10 scale, with red indicating the highest frequencies of occurrence.
Fig. 8. The asymmetry parameter at 0.65 mm as a function of effective
diameter for MODIS Collection 5 (red), the general habit mixture
(black), solid columns (cyan), and the aggregate of solid columns
(green).
models, and (c) the GHM and solid column model. For all
three comparisons, the differences in optical thickness are
very small, indicating that there is little sensitivity in the
mid-IR (8–12 mm) to the choice of habit.
We now turn attention to solar-based optical thickness
retrievals. Before showing results from the fast model,
some insight can be gained by inspection of the asymmetry parameter at 0.65 mm for four different habit models.
As shown in Fig. 8, the MODIS Collection 5 model has the
highest asymmetry parameter values overall due to the
assumption of smooth particles, and the values increase
with particle size. The other three models assume the use
of severely roughened particles, and the asymmetry parameter is lower for these models relative to the MODIS
Collection 5 model. The model based on the aggregate of
solid columns has the lowest values. Note that the value is
fairly constant at 0.76 and invariant with particle size.
A higher value of the asymmetry parameter means that
there is more energy in the forward scattered direction
and less at side- and backscattering angles. This means
B.A. Baum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
133
Fig. 9. Comparison of ice cloud optical thicknesses based on a fast model that infers optical thickness by minimizing the differences between model
simulations and observations at 0.86 and 2.13 mm (MODIS bands 2 and 7, respectively). Results are shown that are based on different ice habit models for
the MODIS granule shown in Fig. 3. Histograms are shown to compare results in (a) MODIS Collection 5 and the aggregate of solid columns, (b) the solid
column and the aggregate of solid column models, (c) the general habit mixture and the aggregate of solid column models, and (d) the general habit
mixture and solid column models. The histograms indicate frequencies of occurrence on a log 10 scale, with red indicating the highest frequencies of
occurrence.
that more scattering will be required from the cloud to
match a given reflectivity, and the increased scattering
results in a higher inferred optical thickness. For a given
set of measured reflectivities, the use of the MODIS
Collection 5 model will result in higher inferred optical
thicknesses than those inferred using the aggregate of
solid column model.
Optical thickness results from the solar-channel fast
model [41] are shown in Fig. 9 for the ice clouds in the
image shown in Fig. 6. The panels in this figure show
histograms of frequency of occurrence for retrievals based
on the various ice habit models. To ease the interpretation
of the results, a 1:1 line is included, and the visible optical
thickness range of the results is limited to 10. Fig. 9 shows
histograms to compare results in MODIS Collection 5 and
the ASC (Fig. 9a), the SC and the ASC models (Fig. 9b), the
GHM and ASC models (Fig. 9c), and the SC and GHM
models (Fig. 9d). In Fig. 9a, note that the differences
between the MODIS C5 and ASC models tend to increase
with optical thickness, and there is a consistent bias in
which the MODIS C5 optical thickness values are higher
than those from the severely roughened aggregate of
solid columns. Similar features are shown in Fig. 9b in the
comparison of optical thickness values between the solid
column model and the aggregate of solid column model.
This is consistent with the asymmetry parameter being
higher for the solid columns than for the aggregate of solid
columns as shown in Fig. 5. Fig. 9c indicates that the optical
thickness values for the GHM are higher than those inferred
from use of the aggregate of solid columns. In fact, the GHM
and solid column models have very similar values for the
asymmetry parameter, so it is not surprising that the optical
thickness values are also similar as shown in Fig. 9d.
The next step is to focus on the low optical thickness
results to compare the IR- and solar-based optical thicknesses as shown in Fig. 10. A comparison of MODIS
Collection 5 τ values between the solar and IR approaches
is shown in Fig. 10a. As noted in earlier studies (e.g., [24]),
the MODIS Collection 5 optical thicknesses are higher
than those obtained by PARASOL. The τ values are limited
in this figure compared to the solar-model results in Fig. 9
since the IR approach lacks sensitivity at higher values.
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B.A. Baum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
Fig. 10. Comparison of ice cloud optical thicknesses inferred separately from MODIS solar and IR bands. The results are based on different ice habit models
for the MODIS granule shown in Fig. 3. Histograms are shown to compare results in (a) MODIS Collection 5 and the general habit mixture, (b) the general
habit mixture, (c) the solid column model, and (d) the aggregate of solid column model. The histograms indicate frequencies of occurrence on a log 10 scale,
with red indicating the highest frequencies of occurrence.
In Fig. 10a–c, the solar-based retrievals tend to be higher
than the IR-based retrievals. However, given that the
asymmetry parameter for the solid column, aggregate of
solid column, and general habit mixture models are lower
than that for Collection 5, the differences between the
solar- and IR-based models decrease as expected. The
aggregate of solid columns compares best with the IRbased retrievals, although the results suggest that the
differences can increase as optical thickness increases.
4. Selected model results
The results in this section are provided separately for
the shortwave region (0.2–5 mm) and longwave region
(3.3–100 mm, or 100–3000 cm " 1).
Fig. 11 shows the model bulk single scattering properties obtained using the general habit mixture with
severely roughened particles for the extinction efficiency,
single scatter albedo, and asymmetry parameter as a
function of wavelength and Deff. The extinction efficiency
is generally slightly above 2 when Deff ¼10 mm and
λ o2.6 mm, but approximately 2 for higher values of Deff.
The scattering is conservative at non-absorbing wavelengths (ω~ ¼ 1 for λ o1.4 mm) but decreases at higher
wavelengths when absorption increases within the ice
particles. The asymmetry parameter tends to increase with
Deff. At 0.65 mm, the asymmetry parameter ranges from
0.77 to 0.81.
Fig. 12 shows the differences in these same properties
between the GHM and SC models. The largest differences
in extinction efficiency are noted at wavelengths between
2.5 and 3 mm. Relatively small differences are noted for the
single scatter albedo, with differences no larger than 0.05
at any wavelength. The asymmetry parameter is shown to be
slightly higher (by about 0.01) for the GHM models compared
to the SC models at wavelengths below about 2.7 mm.
Similar results are shown in Fig. 13 for differences
between the GHM and ASC models. It is apparent that
Fig. 11. Spectral results in the shortwave spectral region (0.2–5 μm) obtained using the general habit mixture with severe particle roughening for
(a) extinction efficiency, (b) single scatter albedo, and (c) asymmetry parameter for effective diameters Deff of 10 mm, 40 mm, and 80 mm.
Fig. 12. Differences between the GHM and the solid column models in the shortwave spectral region (0.2–5 mm) for (a) extinction efficiency, (b) single scatter
albedo, and (c) asymmetry parameter for effective diameters Deff of 10 mm, 40 mm, and 80 mm. Severely roughened particles are assumed for the models.
Fig. 13. Differences between the GHM and the aggregate of solid column models in the shortwave spectral region (0.2–5 mm) for (a) extinction efficiency,
(b) single scatter albedo, and (c) asymmetry parameter for effective diameters Deff of 10 mm, 40 mm, and 80 mm. Severely roughened particles are assumed
for the models.
Fig. 14. Spectral results in the longwave spectral region (100–3000 cm " 1) obtained using the general habit mixture (GHM) with severe particle roughening
for (a) extinction efficiency, (b) single scatter albedo, and (c) asymmetry parameter for effective diameters Deff of 10 mm, 40 mm, and 80 mm.
B.A. Baum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
137
Fig. 15. Differences between the GHM and the aggregate of solid column models in the longwave spectral region (100–3000 cm " 1) for (a) extinction
efficiency, (b) single scatter albedo, and (c) asymmetry parameter for effective diameters Deff of 10 mm, 40 mm, and 80 mm. Severely roughened particles are
assumed for the models.
the asymmetry parameter is much larger for the GHM
than for the aggregate of solid columns.
Results are shown in Fig. 14 at wavenumbers (ν) from
100 to 3000 cm " 1 for the GHM, again assuming severe
particle roughening. It has been shown earlier that roughening is not an issue in the mid-IR, nor is the choice of
habit as important because of increased absorption within
the ice particles. The increased absorption reduces the
differences between the various ice habits that are found
at solar wavelengths. The extinction efficiency (really the
absorption efficiency at these long wavelengths) is close to
2 at wavenumbers between 1400 and 3000 cm " 1. With
the various bulk properties, there is noted a dependence
on Deff at the lower wavenumbers. The results here
indicate that there is some potential in the Far-IR
(100 rνr500 cm " 1) for inferring ice cloud properties
for clouds containing smaller particles.
Fig. 15 shows that the differences are fairly small
between the GHM and aggregate of solid column models.
The only deviations of note are for the Deff models at 10 mm
at Far-IR wavelengths. Similar results are not shown
between the GHM and the solid column model because
the differences are very small.
5. Summary and conclusions
Ice cloud bulk scattering models are derived for 445
discrete wavelengths between 0.2 mm and 100 mm. The
methodology for deriving these optical models is reported
in Baum et al. [1] and is based on microphysical data from
11 field campaigns using a variety of in situ probes, and
incorporates a correction to mitigate the impact of ice
particles that shatter at the probe inlets. The models are
also based on a new library of ice habit single scattering
properties developed for plates, droxtals, hollow and solid
columns, hollow and solid bullet rosettes, an aggregate of
solid columns, and a small/large aggregate of plates [33].
Three sets of models are developed that assume the use of
solid columns only, the aggregate of solid columns only,
and a general habit mixture that involves all nine habits.
The consistency of the resulting models is explored
through comparison with in situ measurements and sensors in the NASA A-Train constellation. The microphysical
properties of IWC and Dmm for each of the assumed habit
distributions is compared to those obtained from in situ
measurements. The solid columns compare most closely
with the in situ microphysical data, while those based on
the general habit mixture are generally within a factor of 2
or better. The aggregate of solid column model underestimates IWC especially at low values, and overestimates
Dmm at high values.
Another test of model consistency is to compare the
polarization properties based on the models to those measured from PARASOL. The habit mixture provides close agreement with measured polarized reflectivities for all effective
diameters Deff and for four days of data from different seasons.
However, neither the solid column nor the aggregate of solid
column models compare as closely at any Deff.
A final consistency test is to investigate the agreement
in optical thickness obtained at solar and IR wavelengths.
138
B.A. Baum et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 123–139
The IR models are not sensitive to habit because of the
stronger absorption within the particles. The solar models
are much more sensitive to habit. A test is performed for a
MODIS scene over the Bay of Bengal. The aggregate of solid
columns provides the closest agreement; this is most
likely due to this habit having the lowest asymmetry
parameter of all the habits that is nearly constant with
Deff at about 0.76.
Finally, spectral results are presented for the shortwave
and longwave models. The various parameters are now
smooth across the spectrum, and do not suffer from
spectral gaps or discontinuities in properties that were
caused, in earlier models, in transitioning from one scattering model to another across the range of particle sizes
and wavelengths.
Bryan Baum, Andy Heymsfield, and Ping Yang gratefully
acknowledge the support provided through NASA Grants
NNX11AR06G and NNX11AF40G. The authors thank Dr. Hal
Maring for his encouragement and support over the years.
We also gratefully acknowledge the anonymous reviewers
for their time and effort in helping us improve this
manuscript.
Appendix A
Bulk microphysical properties
For a given particle size distribution (PSD), the total
projected area and total volume of ice per unit volume of
air are given by
M
Atot ¼ ∑
h¼1
"
Dmax
Ah ðDÞf h ðDÞnðDÞ dD ;
ðA:1Þ
"
V h ðDÞf h ðDÞnðDÞ dD ;
ðA:2Þ
Dmin
and
M
V tot ¼ ∑
h¼1
!Z
Dmax
Dmin
ðA:5Þ
Spectral bulk scattering properties
In this section, the single-scattering properties are
derived at a specific wavelength following [1]. Examples
are provided here for selected parameters. The mean
extinction cross section is given by
R Dmax M
½∑h ¼ 1 sext;h ðD; λÞf h ðDÞ)nðDÞ dD
D
sext ðλÞ ¼ min R D
:
ðA:6Þ
max
M
Dmin ½∑h ¼ 1 f h ðDÞ)nðDÞ dD
The scattering cross section is calculated similarly. The
single-scattering albedo ω is determined by the ratio of the
mean scattering and extinction cross sections:
Acknowledgments
!Z
The effective diameter Deff [43] is defined as
hR
i
Dmax
M
3 ∑h ¼ 1 Dmin V h ðDÞf h ðDÞnðDÞ dD
3 V tot
hR
i ¼
:
Def f ¼
Dmax
2 ∑M
2 Atot
Ah ðDÞf h ðDÞnðDÞ dD
h ¼ 1 Dmin
respectively, where Dmin and Dmax describe the minimum
and maximum particle sizes in the distribution, fh(D) is the
ice particle habit fraction of habit h for size D, n(D) is
the number distribution for size D, and Ah(D) and Vh(D) are
the projected area and volume of a specific particle of
habit h for size D, respectively. The habit fraction is defined
so that for each size bin,
M
∑ f h ðDÞ ¼ 1:
ðA:3Þ
h¼1
ωðλÞ ¼
ssca ðλÞ
sext ðλÞ:
The scattering phase function PðΘÞ is given by
R Dmax M
½∑h ¼ 1 P h ðΘ; D; λÞssca;h ðD; λÞf h ðDÞ)nðDÞ dD
D
P ðΘ; λÞ ¼ min R D
;
max
M
Dmin ½∑h ¼ 1 ssca;h ðD; λÞf h ðDÞ)nðDÞ dD
where Θ is the scattering angle.
The asymmetry parameter (g) is given by
R Dmax M
½∑h ¼ 1 g h ðD; λÞssca;h ðD; λÞf h ðDÞ)nðDÞ dD
D
gðλÞ ¼ minR D
:
max
M
Dmin ½∑h ¼ 1 ssca;h ðD; λÞf h ðDÞ)nðDÞ dD
ðA:7Þ
ðA:8Þ
ðA:9Þ
Narrowband bulk scattering properties
To build narrowband bulk single-scattering properties
appropriate for an imager such as MODIS, the spectral
single-scattering properties need to be integrated over a
spectral response function. An example is provided for
calculating the asymmetry parameter; the other parameters are integrated similarly.
R λmax
gðλÞF s ðλÞSðλÞ dλ
λ
⟨g⟩ ¼ min
;
ðA:10Þ
R λmax
λmin F s ðλÞSðλÞ dλ
where S(λ) is the solar irradiance at solar wavelengths (but
this term switches to the Planck function in the IR,
assuming a cloud temperature of 233K) and Fs(λ) is the
spectral response function. In this study, the Thuillier solar
spectrum is used for integrating over the spectral response
functions [44].
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IWC ¼ ρice ∑
h¼1
!Z
Dmax
Dmin
"
V h ðDÞf h ðDÞnðDÞ dD ;
where ρice ¼0.917 g cm " 3.
ðA:4Þ
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